The processing of semiconductor wafers can use micro-photolithography to imprint patterns of light onto a light sensitive photoresist. Depending on the type of photoresist, either that portion of the photoresist that was exposed to light, or that portion of the photoresist that was not exposed to light is then removed, leaving either a positive or negative image of the pattern. The photoresist may then be used as a mask for the deposition or removal of material used to form the components and interconnections of a circuit on the wafer. This photolithography process is repeated many times with additional patterns and masks during fabrication of integrated circuits on the wafer.
Maintaining an accurate focus of the pattern of light on the wafer is particularly important in the above process. The size of features on a typical semiconductor wafer are sufficiently small that a minimal change in the focus can blur a pattern sufficiently to cause separate portions of the pattern imprinted on the wafer to overlap. In such case, material will be improperly deposited or removed on areas of the wafer.
The pattern of light is typically focused onto the wafer using a device known as a "stepper." One such stepper is manufactured by ASML. The stepper contains a set of lenses (hereinafter referred to simply as ("a lens") that is used to focus the pattern of light onto the wafer. The light passing through the lens heats the lens, thereby expanding the lens and changing its focal length. Thus, even if the image is precisely focused at the start of an exposure, it will subsequently be out of focus.
The amount of expansion of the lens, and therefore the change in focus, will vary depending on factors such as the intensity of the light, the reflectance of the wafer, the duration that the light is on the lens, as well as other factors.
FIG. 1 is a graph of the actual change in focus of the lens in a stepper machine manufactured by ASML as a function of time as the lens heats up. Those skilled in the art will be familiar with stepper machines, including the ASML stepper, and further discussion is therefore omitted, in the interest of brevity. As seen in FIG. 1, over a period of approximately half an hour (typically the time used to process 25 wafers) the focus of the lens in the stepper changes by approximately 0.4 microns. This change is significant given that typically an entire depth of field for the focus may be only 0.4 microns. The heating, and therefore the expansion of the lens, is not constant due to brief cooling periods while a processed wafer is removed and an unprocessed wafer is inserted under the lens. During these times no light is being applied to the lens. These cooling periods can be seen periodically in FIG. 1 by the slight decreases in the focus signal.
FIG. 2 is a graph of a formula used to compensate for lens heating in an ASML stepper. Rather than measuring the change in focus after each wafer is processed and correcting for that change in focus, the ASML stepper uses the estimate of the change in focus shown in FIG. 2 to alter the focus of the lens as the lens heats up during a series of exposures. For example, if the focal length of a lens increases by 0.4 microns over a period of 30 minutes, the stepper can be programmed to decrease the focus of the stepper by 0.4 microns over this 30 minute period.
The estimated change in focus shown in FIG. 2 is given by the mathematical formula F(inf)=[(u.sub.1.times.T.times.S.times.Q).times.(1-exp(-t/.tau..sub. 1))+(u.sub.2.times.T.times.S.times.Q).times.(1-exp(-t/.tau..sub.2))] (Equation 1), where F(inf) is the focus of the lens, u.sub.1 is a first scaling machine constant, u.sub.2 is a second scaling machine constant, T is a transmission value of a reticle in the stepper, S is a field size of the image (i.e., how much of the lens is illuminated), Q is an intensity of the light, t is a duration the light is on the lens, .tau..sub.1 is a first time machine constant, and .tau..sub.2 is a second time machine constant. Each of these variables is empirically determined, and programmed into the ASML stepper. The ASML stepper then adjusts the focus of the stepper according to the above formula to compensate for the heating induced change in the focal length of the lens.
One problem with the above-described compensating method is that it does not account heating induced expansion of the lens due to the variations in the light reflected from the wafer. More specifically, a lighter wafer reflects more light back to the lens than will a darker wafer. The lens will thus be heated more rapidly when the stepper is making an exposure on a lighter wafer than it will when the stepper is making an exposure on a darker wafer. This focus error can result in a blurred pattern being imprinted on the wafer even where the compensation technique described above is used.
Further, steppers have only specific input variables that can be adjusted to determine the focus of the lens. Therefore, even if a magnitude of wafer reflectance were determined, the reflectance could not be programmed into the stepper. For example, the formula discussed above has eight variables, each of which is attributable to a specific characteristic of the stepper machine, it's related components, or functions thereof. The stepper may be programmed with each of these variables and no more. The stepper is incapable of processing additional variables, such as the reflectance of the wafer.